Estimating characteristics of a transmission channel is a particularly important task in the field of wireless communications, for producing receivers of digital signals characterized by a small probability of incorrect recognition of transmitted symbols. Typically, in wireless communications the transmitted signals fade according to a time-variable fading coefficient that must be estimated for correctly recognizing transmitted symbols. For this reason receivers that use the so-called “channel estimators” have been produced.
According to a known technique, certain channel estimator algorithms contemplate the step of sending a pre-established sequence of known symbols to the receiver, commonly called a “training sequence”, on the transmission channel the characteristics of which need to be estimated. The relative fading coefficient is estimated in function of the received signal.
Known receivers have a quite complex hardware for estimating the channel characteristics. They commonly use Kalman filters and determine fading coefficients using a relatively long “training sequence”. Kalman filters have drawbacks because they introduce a significant delay in the estimation of the fading coefficients, thus these receivers require a faster system of estimation of the channel characteristics.
FIG. 1 shows a typical “channel estimating algorithm” disclosed in Grant “Joint Decoding and Channel Estimation for Space-Time Codes”. The demodulator tracks the channel, that is it adapts itself to the varying characteristics of the channel. This operation is very important in communications implementing the so-called “transmit diversity” technique disclosed in S. M. Alamouti “A simple Transmit Diversity Technique for Wireless Communications.” IEEE Journal on Select Areas in Communications, Vol. 16 No. 8 October 1998.
According to the “transmit diversity” technique, a time correlation among symbols transmitted with a plurality of antennas is introduced. Each antenna transmits on a transmission channel with fading characteristics that in general differ from those of the transmission channel of any other antenna. To correctly receive the transmitted signals, it is not possible to ignore the different fading coefficients of the channels in use, if satisfactory performances are to be obtained. Indeed, the fading coefficient of each channel may vary with time especially if the receiver is moving and/or the transmission is at high bit-rate. To better illustrate the problem, the “transmit diversity” technique is briefly discussed below.
TRANSMIT DIVERSITY. Noise is always supposed to be Gaussian in designing digital receivers. According to this hypothesis, the bit-error rate (BER) is supposed to be reduced by 10−3 to 10−4 s, thus increasing the signal-to-noise ratio of 2 or 3 dB. Actually, because of the so-called “multi-path fading” phenomenon, it is necessary to increase the signal-to-noise ratio of about 10 dB for reducing the BER from 10−3 to 10−4.
The “transmit diversity” technique allows a reduction of the minimum signal-to-noise ratio of the received signals necessary for having a satisfactory BER. Alamouti demonstrated that a system with two transmitting antennas and a receiving antenna has the same yield of a receiver, shown in FIG. 2, with two antennas. The receiver proposed by Alamouti, shown in FIG. 3, has the same performances with the same “data rate” of the receiver of FIG. 2.
More particularly, Alamouti proposed to transmit symbols s0 and s1 with two different antennas according to the following rule
      [                                        s            0                                                s            1                                                            -                          s              1              *                                                            s            0            *                                ]     wherein the symbol at row n and column j is to be transmitted during the n-th symbol interval by the j-th antenna. The asterisk indicates the complex conjugate of the symbol. In practice, according to the technique disclosed in Almouti, the symbols s0 and s1 are transmitted in the first symbol interval by the first and by the second antenna, respectively, while in the second symbol interval the pair of symbols −s1*, s0 * are transmitted by the first and by the second antenna, respectively.
The receiver has only one antenna. The two channels fade the transmitted signals according to the coefficients h0 and h1, thus the following signal r is received:r=h0·s0+h1·s1+n0 The receiver detects and decodes the symbols by processing the received signal with a maximum likelihood algorithm, for two consecutive symbol intervals.
The fading coefficients of the transmission channels have a module and a phase:h0=α0·eiθ0 h1=α1·eiθ1 wherein i is the imaginary unit.
According to a simple model, the modules of these fading coefficients are stochastic variables with a Rayleigh distribution, while the phases are uniformly distributed in the interval [0, 2π]. An ideal receiver provides an estimation of the fading coefficients h0 and h1 and it functions correctly if this estimation is exact. The fact that the module of the fading coefficient of a channel is a stochastic variable with a Rayleigh distribution is only one of the possible mathematical models that may be adopted. According to other authors, these modules must be modeled as stochastic variables with a Rice or Jakes distribution. If the transmission channel presents characteristics different from the ideal characteristics of the chosen stochastic distribution, the bit-error rate of the receiver could be not satisfactory.
U.S. Pat. No. 6,603,823 discloses a “channel estimator” that is quite complex and slow and that processes values of received data with a priori determined probabilities only on the received symbols. U.S. Pat. No. 5,838,739 discloses a classic correlation estimator. The system needs a sequence of synchronization symbols. The received signal is oversampled and compared (through “correlation blocks”) with certain sequences (DATA WORD) that strongly depends on the mathematical model of the channel, that is-they depend on its statistic figure.
U.S. Pat. No. 6,327,314 discloses a “channel estimator” based on time and frequency correlations of the frequency responses of the transmission channels. U.S. Pat. No. 6,269,131 discloses an adaptive equalizer that implements the minimum squares algorithm. It needs test symbols and a processing unit. U.S. Pat. No. 5,737,327 discloses a “channel estimator” for CDMA based on the use of a pilot channel for estimating the phase and the fading of the transmission channel. U.S. Pat. No. 5,712,877 discloses a device for transmitting and receiving digital information by inserting “training sequences” or pilot symbols inside a data stream transmitted in CPM. This implies that the pilot symbols depend on the previously transmitted data according to the coding rule used for the CPM. Channel estimation is carried out with an iterative method that improves this estimation, based on the transmitted pilot symbols, at each iteration.
U.S. Pat. No. 5,272,727 discloses an adaptive decoder that estimated the characteristics of the transmission channel for obtaining a sequence of transmitted symbols by processing a received signal. The estimation of the channel fading is updated in function of the error signal and a LMS algorithm. This error signal is obtained by comparing a properly delayed (i.e. stored) replica of the sequence of samples with a signal obtained by convolution of the estimated sequence of data from the MLSE (depending on the same samples) with the pulse response estimated at the previous step. Depending on this comparison it is decided whether repeating the operation of data decoding using the new channel estimation or not.
U.S. Pat. No. 5,303,263 discloses an equalizer comprising a “channel estimator” having a processor that implements the Viterbi algorithm for estimating accurately the transmitted symbols. It uses a RLS algorithm for updating the channel coefficients. An error signal is generated by comparing the stored sequence of samples with the signal obtained by convolution between the current estimation of the pulse channel response and the relative sequence of data estimated by the decoder.
European patent EP 369 406 discloses a PSK demodulator in which the received PSK signal is phase-locked by means of an algorithm for maximizing the signal-to-noise ratio or minimizing the bit-error rate. European patent EP 317 127 discloses a time-varying “trellis-code” modulation technique and a related device that allows PSK transmissions with high performances, in particular for radio transmissions. European patent application No. 03425662.8 (EP 1 542 772) in the name of the same Assignee discloses a process and a relative system for decoding signals comprising symbols coded in respective symbol intervals that modulate a carrier, very easy to be realized and not computationally onerous.
Other pertinent background references include: Kang M. P. Fitz and S. B. Gelfand, “Blind Estimation of Multi-path Channel Parameters: A Modal Analysis Approach” IEEE Transaction on Communications Vol. 47 No. 8 1999; G. J. Foschini and M.J. Gans “On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas” Wireless Personal Communications© 1998 Kluwer Academic Publishers; P. Alexander and A. Grant “Iterative Decoding and Channel Estimation” ISIT Sorrento June 2000; C. Tellambura, M. G. Parker, Y. Jay Guo, Simon J. Shepherd, and Stephen K. Barton “Optimal Sequences for Channel Estimation Using Discrete Fourier Transform Techniques IEEE Transaction On communications, Vol. 47, No. 2, 1999; Komninakis, C. Fragouli, A. H. Sayed, R. D. Wesel, “Channel estimation and equalization in fading”; U.S. Pat. No. 6,603,823, “Channel Estimator”, in the name of Intel Corporation; J. G. Proakis, “Digital Communication”, Third Edition, McGraw-Hill Int. Ed; S. Bendetto, E. Biglieri, V. Castellani “Digital Transmistion Theory”; and B. Vucetic, J. Yuan, “Space-Time Coding”, Wiley.